How am I supposed to handle muscle deformation while rigging?
Unfortunately what you're asking about is a very broad and difficult topic and there isn't a very straightforward answer for Blender. I myself have done some research on it for team projects and can share what I have found.
Modeling muscle deformations is no easy task in 3D software. Large studios such as Pixar will often run complex simulations that account for elasticity and the like to create realistic forms. Blender doesn't natively support these capabilities, at least not to the extent of realism that these studios have.
There are (often expensive) add-ons available, such as X-Muscle System, which can run physical simulations for organic tissue. You could also write python scripts to do this yourself (though who knows how long that could take.) Personally I've never used either of these approaches, so I can't vouch for the benefits of either.
Even if we don't have an excess of time or money, hope is not lost. The most common approach I've seen is using shape keys, often called &quot;Corrective Shape Keys.&quot; Here's the general idea:

Create your rig as normal. A cool trick is to not have the armature deform the mesh itself, but rather have it deform a mesh lattice/cage, which in turn deforms the mesh. This often results in smoother deformations and is used in many advanced rigging tools such as Juan Pablo Bouza's BlenRig.

Now, on the base mesh, create a shape key for each joint whose muscle deformation you want to adjust. For instance, your reference picture, you'd probably want a shape key for each knee, elbow, shoulder, and the torso.

For each shape key, bend the joint to the extreme and edit the mesh so that it looks you'd want it. This can be done in edit or sculpt mode (but don't edit the topology!)

Using Drivers, drive the factor of the shape keys with the rotation of the corresponding joint. This can be tricky to get right sometimes. With the knee for instance, you'd want the factor of the shape key to be greater when the knee is bent and around zero when in rest pose.


If you prefer video resources, this YouTube video has a good demonstration of corrective shape keys and this one is a decent introduction to using drivers.